Poisson kernel of half spaces in real hyperbolic spaces

Abstract : We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space $\H^n$. This enables us to find asymptotic properties of the kernel. We also show convergence to the Poisson kernel of the whole space $\H^n$. For n=3, 4 or 6 we compute explicit formulas for the Poisson kernel itself.
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Submitted on : Thursday, June 8, 2006 - 7:41:40 PM
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Tomasz Byczkowski, Piotr Graczyk, Andrzej Stos. Poisson kernel of half spaces in real hyperbolic spaces. Revista Matemática Iberoamericana, European Mathematical Society, 2007, 23 (2007), no. 1, pp.85--126. ⟨hal-00079091⟩

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